**1.** Without doing any calculations,
explain why a pie chart and a bar chart would both be poor choices for displaying
these data on the number of U.S. commercial banks of different sizes.

Assets (Dollars) | Number of Banks |

0 to 24.9 million | 3,330 |

25 to 49.9 million | 3,145 |

50 to 99.9 million | 2,782 |

100 to 499.9 million | 2,461 |

500 to 999.9 million | 253 |

1 to 2.9 billion | 202 |

3 to 9.9 billion | 172 |

**2.** Carefully explain the
error in this statistical argument by Henry Van der Eb, president of the Mathers
Fund, for why stock prices are due to fall: "We've been spoiled by huge stock
returns; in order to return to the [long-term] mean of 9.7% returns, we must
have some down years." [quoted in Craig Torres, "Three Cash-Laden Bears See
End of Bulls' Run," The Wall Street Journal, August 4, 1992.]

**3.** Answer this job-interview
question that was asked this year: "You are playing tennis against someone who
is not as good as you. Assuming that the games are independent and that your
probability of winning any game is constant and greater than 0.5, are you more
likely to win more games than your opponent if you play 5 games or if you play
10 games?" Explain your reasoning.

**4.** Here is a job-interview
question that was asked this year: "There is a 60% chance of rain on Saturday
and a 40% chance of rain on Sunday. What is the probability that it will not
rain this weekend." The interviewer said that the correct answer is (1 - 0.6)(1
- 0.4) = 0.24. The job candidate said that the correct answer is 1 - 0.6(0.4)
= 0.76. What do you say?

**5.** Answer this job-interview
question that was asked last year: "A box contains 20 pennies, of which 19 are
normal coins with a head on one side and tail on the other; one coin has heads
on both sides. The box is shaken until the coins are mixed thoroughly. Then
one coin is randomly selected and flipped five times. Each time it lands heads.
What is the probability that it is the two-headed coin?"

**6.** Answer this centuries-old
question that the Chevalier de Mere asked Blaise Pascal: Two-evenly matched
players are playing a sequence of games. The first person to win 4 games wins
$1000. They have played 4 games and A has won 3 games and B has won 1 game.
At this point they are forced to stop playing. How should they divide the $1000,
so that each person receives the expected value of what they would have won
had they continued playing?

**7.** An article in the San
Francisco Chronicle [September 6, 1984] suggested that AIDS may be caused by
drinking fluoridated water: "While half the country's communities have fluoridated
water supplies and half do not, 90 percent of AIDS cases are coming from fluoridated
areas and only 10 percent are coming from nonfluoridated areas." Why are these
data unpersuasive? Be specific.

**8.** A school estimated the
average number of school-age children per family having school-age children
by questioning each child in the school and calculating the mean of their answers.
Was their estimate too high or too low? Use a simple numerical example to explain
your reasoning.

**9.** The random walk hypothesis
says that the probability that stock prices will increase today is independent
of the behavior of stock prices on other days. If, on any given day, there is
a 0.52 probability that the Dow Jones Industrial Average will go up and a 0.48
probability that it will go down (and no chance that it will be unchanged),
what is the probability that during the course of a year with 250 trading days
the Dow will have more up days than down days? Use a normal approximation.

**10.** Identify several problems
that prevent this graphic from conveying useful information [The Student Life
December 11, 1996.]: